Accurate and efficient Nyström volume integral equation method for the Maxwell equations for multiple 3-D scatterers

Abstract

In this paper, we develop an accurate and efficient Nyström volume integral equation (VIE) method for the Maxwell equations for a large number of 3-D scatterers. The Cauchy Principal Values that arise from the VIE are computed accurately using a finite size exclusion volume together with explicit correction integrals consisting of removable singularities. Also, the hyper-singular integrals are computed using interpolated quadrature formulae with tensor-product quadrature nodes for cubes, spheres and cylinders, that are frequently encountered in the design of meta-materials. The resulting Nyström VIE method is shown to have high accuracy with a small number of collocation points and demonstrates p-convergence for computing the electromagnetic scattering of these objects. Numerical calculations of multiple scatterers of cubic, spherical, and cylindrical shapes validate the efficiency and accuracy of the proposed method.